Open AccessGenuine monogamy relations in no-signaling theories—a geometric approach
Author(s) -
Junghee Ryu,
Daemin Lee,
Jinhyoung Lee,
Paweł Kurzyński,
Dagomir Kaszlikowski
Publication year - 2021
Publication title -
new journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.584
H-Index - 190
ISSN - 1367-2630
DOI - 10.1088/1367-2630/abf2fb
Subject(s) - multipartite , class (philosophy) , bipartite graph , physics , simple (philosophy) , probabilistic logic , pure mathematics , type (biology) , qubit , quantum , theoretical physics , discrete mathematics , quantum mechanics , mathematics , epistemology , computer science , quantum entanglement , artificial intelligence , graph , ecology , philosophy , biology , statistics
Quantum correlations are subject to certain distribution rules represented by so-called monogamy relations. Derivation of monogamy relations for multipartite systems is a non-trivial problem, as the multipartite correlations reveal their behaviors in a way different from bipartite systems. We here show that simple geometric properties of probabilistic spaces, in conjunction with no-signaling principle, lead to genuine monogamy relations for a large class of Bell type inequalities for many qubits. The term of ‘genuine’ implies that only one out of N Bell inequalities exhibits a quantum violation. We also generalize our method to qudits. Using the similar geometric approach with a quasi-distance employed, we derive Svetlichny–Zohren–Gill type Bell inequalities for d -dimensional tripartite systems, and show their monogamous nature.